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arXiv · 1811.07365

Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures

Jerzy Lukierski·Stjepan Meljanac·Mariusz Woronowicz
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Abstract

We consider the generalized (10+10)-dimensional D=4 quantum phase spaces containing translational and Lorentz spin sectors associated with the dual pair of twist-quantized Poincare Hopf algebra $\mathbb{H}$ and quantum Poincare Hopf group $\widehat{\mathbb{G}}$. Two Hopf algebroid structures of generalized phase spaces with spin sector will be investigated: first one $% \mathcal{H}^{(10,10)}$ describing dynamics on quantum group algebra $% \widehat{\mathbb{G}}$ provided by the Heisenberg double algebra $\mathcal{HD=% }\mathbb{H}\rtimes \widehat{\mathbb{G}}$, and second, denoted by $\mathcal{% \tilde{H}}^{(10,10)}$, describing twisted Hopf algebroid with base space containing twisted noncommutative Minkowski space $\hat{x}_{μ}$. We obtain the first explicit example of Hopf algebroid structure of relativistic quantum phase space which contains quantum-deformed Lorentz spin sector.

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Jerzy Lukierski, Stjepan Meljanac, Mariusz Woronowicz. 2018-11-18. Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures. https://doi.org/10.1016/j.physletb.2018.11.055

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